Time dependent magnetic field gradients are employed in most magnetic resonance imaging (MRI) and localized spectroscopy techniques. In an MRI technique, magnetic fields are rapidly switched according to a desired pattern. In order to receive good results, the generated magnetic fields must accurately follow the desired pattern. Substantially all MRI systems include conductive materials which form eddy currents responsive to the switched magnetic field. These eddy currents induce a time dependent magnetic field, referred to as an eddy field, which distorts the generated magnetic fields. Generally, the generated magnetic field includes a constant field B.sub.0 and gradient fields in three directions labeled Bx, By and Bz. The gradient fields are generated by passing currents through coils.
One of the methods used to eliminate the effect of the eddy fields, is eddy current pre-compensation. In pre-compensation, the currents used to generate the magnetic fields are changed, such that they create in addition to the magnetic fields which follow the desired pattern, a compensation magnetic field which cancels the eddy fields. Generally, a filter is used to change the currents through the coils such that they create the compensation field in addition to the desired magnetic fields. Typically it is assumed that the eddy-fields may be modeled by a sum of decaying exponents. Measurements of the eddy-field are fit into the model, providing an adjusted model. The fitting involves assigning values to parameters of the model (the amplitudes and time constants of the exponents). Parameters of the filter are then adjusted responsive to the adjusted model.
The induced eddy fields do not necessarily have the same spatial distribution as the fields which induced them. Eddy fields which have the same spatial distribution as the field which induced them are referred to as diagonal fields while fields in other directions are referred to as non-diagonal fields. Usually, induced eddy fields include both diagonal and non-diagonal fields and the non-diagonal eddy fields are of much smaller magnitudes than the diagonal fields. In pre-compensation, non diagonal fields are compensated by changing the currents in other coils of the system than the coil used to generate the field which induced the eddy fields.
Eddy current pre-compensation is described, for example, in a paper titled "Reduction of pulsed gradient settling time in the superconducting magnet of a magnetic resonance instrument", by Dye J. Jensen, et al., Medical Physics, Vol. 14, September/October 1987, the disclosure of which is incorporated herein by reference. This paper assumes the eddy-field model is a sum of three exponents, and the filter comprises three high pass filters. The paper states that the time constants and amplitudes of the filters are adjusted interactively starting from the longest time constant.
A paper titled "A programmable Pre-emphasis System" by H. M. Gach et al, MRM 40:427-431, 1998, the disclosure of which is incorporated herein by reference, describes using sixteen RC filters with fixed time constants, to compensate for the eddy fields. The eddy fields are measured separately for each time constant and the amplitude coefficients of the filters are adjusted accordingly. The described method is reported to require anywhere between a few hours to days for measuring and compensating the eddy fields.
U.S. Pat. No. 4,698,591 to Glover et al., the disclosure of which is incorporated herein by reference, describes modeling the field by a sum of two or three exponentials. The time constants and amplitudes of the exponentials are determined in a way which minimizes a .chi..sup.2 error expression. In order to simplify the exponential fit, some of the stages are performed while keeping the time constants at fixed values such that the fit is linear in the amplitudes of the exponentials. The time constants and amplitudes of the exponents of the model are used to set parameters of respective filters. This patent also describes adjusting initial values of the time constants and amplitudes of the filters using an iterative process. The remaining eddy-field after the correction is measured and the measurements are fit to a new set of exponentials using the previous time constants. The resulting amplitudes are added to the previous amplitudes.
A paper titled "Analytical Method for the Compensation of eddy-currents Effects Induced by Pulsed Magnetic Field Gradients in NMR systems", by P. Jehenson et al., Journal of Magnetic Resonance, 1990, pages 264-278, the disclosure of which is incorporated herein by reference, describes fitting the measurements of an eddy field into a model which takes into account the pre-compensation parameters of the filters. The eddy fields are at first measured and fit into the model while the pre-compensation parameters have zero values. Thereafter, the parameters are determined responsive to the model. The compensated eddy fields are then remeasured and are fit into an improved model which includes the applied values of the parameters of the filters. The improved model is used to reset the parameters of the filters. The paper suggests repeating the procedure to yield improved parameters.
A paper titled "Optimization of eddy-Current Compensation", by J. J. Van Vaals and A. H. Bergman, Journal of Magnetic Resonance 1990, pages 52-70, the disclosure of which is incorporated herein by reference, describes performing a plurality of compensation iterations to correct a first fit to the model. The compensation iterations include performing fine adjustments in the measurement method of the eddy fields.
A paper titled "An Algorithm for eddy Currents Symmetrization and Compensation" by Yuval Zur and Saul Stoker, Magnetic Resonance in Medicine, February 1996, the disclosure of which is incorporated herein by reference, suggests an additional filter to symmetrize the eddy field of a pair of coils before it is compensated by the compensation filter. This paper describes a method of measuring the eddy field and accordingly determining the parameters of the compensation filter. The model in this paper includes a sum of one or more exponentials. Due to noise and other errors the process is not accurate and therefore this paper suggests performing an iterative compensation process. However, the calculations used in this paper to determine the parameters of the RF filters based on the measurements are unstable and in the presence of noise do not converge or converge to wrong values.